Just look at this. A cutting edge communications device from an alternative 1950. But designed and fabricated by a person on their workbench, like the raddest cyberpunk street tech.
These started as innocuous doodles which accidentally ended up showing the beauty and fascination in mathematics, but eventually became more elaborate and specific.
Things like this:
In this series she describes hexaflexagons. Watch 'em.
I love people making weird instruments out of weird things. Here’s an organ made out of a matrix of mechanical floppy drives.
You can read more about it on Ars Technica.
Though it's called the "Game" of Life, and some people describe it as a zero-player game, it's not really a game in the traditional sense of the word.
For an unexpected example of an unambiguous game which is also Turing-complete, check out Magic: The Gathering. It has been shown that a Universal Turing machine can be constructed inside Magic, and hence that it is Turing-complete.
I played a lot of Magic in high school, though it's too expensive of a habit to keep up for long. If, like me, you remember Magic fondly, but don't play it so much any more, might I recommend Mark Rosewater's Drive to Work podcast?
Conway's Game of Life is a well-known cellular automaton in which, every tick, the state of each of the cells on a giant grid is determined only by the states of its immediate neighbours in the previous tick. Despite its extremely simple definition, it is famously Turing-complete, which is roughly to say that it can compute any computable function.
And so, of course, someone has written a Life emulator, in Life.
Perhaps it's Life all the way down...
Oh this? Just a film of landing on Mars.
PS. If you haven't seen NASA's "Seven Minutes of Terror" video, it's worth checking out. Those folks are crazy.
This makes me pretty happy. Mike Ando has created a real, working Myst linking book.